The .308 will reach 1000, but it's a moonshot to get it there and you need more than good optics, you need at least 20MOA rail to give you the play to dial in at that distance.
I have shot the .338 Lapua at about 850-900 yards and it's a beast. I don't mind it, but I would not want to shoot it all day, I am man enough to say. That thing flat gets your attention when you touch it off.
Ammo is ridiculous for the Lapua. First off you have the brand name brass and then you have the specialized accurate loads off the shelf. I would not be surprised at all with Jim's price of $115/box. That is just crazy talk for a day of shooting anything BUT bad guys in the worst possible case.
Txhillbilly was reading my mind again. There are a lot of other cartridges out there that will not only reach 1,000 but do it effectively and with purpose upon impact.
6.5 x 284 if the golden child of the benchrest mad scientist brain trust and it's a great round for shooting matches at 1,000. I honestly don't know what kind of impact it hits with because I haven't really studied it. As for accurate, barrel life and ease of shooting, all would rate very good bordering on great. You will most likely have to reload to make effective use of it though, so unless you are set up already, that will add to your overall cost.
I have a 7mm Mag that I had custom built and it came in under $5000 all said and done with glass and a Pelican case. The chamber was cut for Federal Match specs, so I can shoot right off the shelf as reloading isn't something I would consider myself good at yet.
I built this gun heavy so it isn't punishing to shoot. I wouldn't want to hump it for a 60 mile stretch, but once I lay down it's quite nice to pull the trigger and not be kicked too hard.
.300 Win Mag is another viable option. Flat shooting, hard hitting and a ton of options. Ammo is a bit pricey for this one too, but not nearly as bad.
.30-06 is often overlooked, but it really is the rifleman's cartridge. It can be loaded up or down in bullet weight depending on the intended target density, the ammo is everywhere, and it's a nice, polite round to shoot. It will reach 1,000 and I believe it will still have the oomph to do some damage when it gets there. (Carlos Hathcock shot the .30-06 almost for his entire career and was quite effective on "hamburgers and hotdogs" as he referred to them).
As to the weapon in question. Savage is one of those you love it or you don't brands. Loyal following, pretty solid rep. I haven't seen this particular model so I am afraid I don't have much to offer for you there.
Good luck and keep us informed on what you decide.